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Non-Abelian k-vortex dynamics in N = 1* theory and its gravity dual

Roberto Auzzi, Prem Kumar Orcid Logo

Journal of High Energy Physics, Volume: 2008, Issue: 12, Pages: 077 - 077

Swansea University Author: Prem Kumar Orcid Logo

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<p>We study magnetic flux tubes in the Higgs vacuum of the <img src="" alt="Script N" align="BASELINE" /> = 1* mass deformation of SU(<em>N</em><sub>...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: 2008
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Abstract: <p>We study magnetic flux tubes in the Higgs vacuum of the <img src="" alt="Script N" align="BASELINE" /> = 1* mass deformation of SU(<em>N</em><sub><em>c</em></sub>), <img src="" alt="Script N" align="BASELINE" /> = 4 SYM and its large <em>N</em><sub><em>c</em></sub>string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all <em>N</em><sub><em>c</em></sub> we identify a ``colour-flavour locked'' symmetry, SO(3)<sub><em>C</em>+<em>F</em></sub> which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian <em>k</em>-vortex solutions carrying a <img src="" alt="Bbb Z" align="BASELINE" /><sub><em>N</em><sub><em>c</em></sub></sub>-valued magnetic flux, with winding, 0 < <em>k</em> < <em>N</em><sub><em>c</em></sub>. These <em>k</em>-strings spontaneously break SO(3)<sub><em>C</em>+<em>F</em></sub> to U(1)<sub><em>C</em>+<em>F</em></sub> resulting in an <em>S</em><sup>2</sup> moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric <img src="" alt="Bbb C" align="BASELINE" /><img src="" alt="Bbb P" align="BASELINE" /><sup>1</sup> model with a theta angle θ<sub>1+1</sub> = <em>k</em>(<em>N</em><sub><em>c</em></sub>−<em>k</em>)θ<sub>3+1</sub> where θ<sub>3+1</sub> is the Yang-Mills vacuum angle. We find numerically that <em>k</em>-vortex tensions follow the Casimir scaling law <em>T</em><sub><em>k</em></sub> <img src="" alt="propto" align="BASELINE" /> <em>k</em>(<em>N</em><sub><em>c</em></sub>−<em>k</em>) for large <em>N</em><sub><em>c</em></sub>. In the large <em>N</em><sub><em>c</em></sub> IIB string dual, the SO(3)<sub><em>C</em>+<em>F</em></sub> symmetry is manifest in the geometry interpolating between <em>AdS</em><sub>5</sub> <strong>×</strong> <em>S</em><sup>5</sup> and the interior metric due to a single D5-brane carrying D3-brane charge. We identify candidate <em>k</em>-vortices as expanded probe D3-branes formed from a collection of <em>k</em>D-strings. The resulting <em>k</em>-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S-duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in <img src="" alt="Script N" align="BASELINE" /> = 1* theory in the large <em>N</em><sub><em>c</em></sub> limit.</p>
College: Faculty of Science and Engineering
Issue: 12
Start Page: 077
End Page: 077